Thermodynamic analysis and optimization of power cycles using a finite low-temperature heat source.pdf

INTERNATIONAL JOURNAL OF ENERGY RESEARCH

Int. J. Energy Res. 2012; 36:871

885

Published online 9 March 2011 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/er.1839

–

Thermodynamic analysis and optimization of power

cycles using a

temperature heat source

Mohammed Khennich and Nicolas Galanis * , †

nite low

‐

Faculté de génie, Université de Sherbrooke, Sherbrooke, QC, Canada J1K 2R1

SUMMARY

The analysis of a subcritical Rankine cycle with superheating, operating between a constant

owrate low-

temperature heat source and a

nite size

thermodynamics, is presented. The results show the existence of two optimum evaporation pressures: one

minimizes the total thermal conductance of the two heat exchangers, whereas the other maximizes the net power

output. A comparison of such results for

xed temperature sink, according to the principles of classical and

ve working

uids leads to the selection of R141b for a system generating

10% of a reference power which depends on the speci

ed source and sink characteristics; for the conditions under

consideration this reference power is 6861kW. The results for this particular system show that the minimum total

thermal conductance of the two heat exchangers is 1581kWK − 1 ;

the corresponding thermal ef

ciency is 12.6%

and the total exergy losses are 13.8% of the source

s exergy. Slightly more than 50% of the exergy destruction

’

KEY WORDS

waste heat; energy analysis; exergy analysis; heat exchanger conductance; turbine size parameter; Rankine cycle

Correspondence

* Nicolas Galanis, Faculté de génie, Université de Sherbrooke, Sherbrooke, QC, Canada J1K 2R1.

† E-mail: Nicolas.Galanis@USherbrooke.ca

Received 21 October 2010; Revised 11 January 2011; Accepted 23 January 2011

1. INTRODUCTION

thermal energy in combustion gases. Traditional exam-

ples of such applications are the heating of the combus-

tion air supplied to the boilers of steam plants by the ue

gases and the cogeneration installations using the exhaust

gases of a gas turbine plant to produce steam for

industrial processes or for electricity generation.

The energy of thermal engine exhaust gases is not

the only source of low (80 – 150°C) or intermediate

(up to 350°C) temperature heat. Such thermal energy

abounds in nature (geothermal and solar energy) and is

also available as waste heat from industry (pulp and

paper, aluminum production, etc.). The potential

contribution of these sources to our energy needs is

important. An MIT report [1] estimated that it would

be possible to develop 100GW of generating capacity

from geothermal sources in the United States by in-

vesting 1 billion dollars over a period of 15 years.

Another study [2], which analyzed manufacturing

processes within the eight largest Canadian manu-

facturing sectors accounting for approximately 2/3 of

the total energy used by Canadian industries, indicates

that approximately 70% of the input energy is released

to the environment as waste heat. The use of these

energy sources would reduce the dependence on

imported ones and could have a benecial environmental

The availability of abundant quantities of energy is an

essential condition for the well being and development

of our modern industrial societies. As the population

and economic activity increase, the global consump-

tion of energy rises continuously. The principal

primary energy sources that are used to satisfy this

ever ‐ increasing demand in all the economic sectors are

fossil fuels. Although available in large quantities, they

are neither innite nor renewable. Furthermore, the

conversion of their chemical energy into useful work

by combustion and thermal engines, which is almost

the only method used for their exploitation, is subject

to the fundamental laws of thermodynamics which

severely limit the efciency of such systems and results

in undesirable side effects, such as greenhouse gases

(GHGs), urban smog, thermal pollution and acidica-

tion of lakes and rivers. It is therefore imperative

to seek and adopt alternate renewable energy sources

as well as methods, which improve the conversion

efciency and diminish the negative impacts of fossil ‐

fuelled engines. One way of increasing the performance

and decreasing the environmental impact of stationary

thermal engines is by recuperating and utilizing low ‐ grade

871

M. Khennich and N. Galanis

Thermodynamic analysis and optimization of power cycles

effect. Thus, the theoretical GHG reduction that can be

achieved by recovering the above ‐ mentioned waste heat

from the eight largest Canadian manufacturing sectors is

2.5 times the target of 45Mt of GHG suggested by the

Kyoto protocol.

The methods that can be used to convert this thermal

energy into mechanical energy and electricity include

thermodynamic cycles using organic uids (ORC),

mixtures of pure uids (NH 3 /H 2 O) and uids with very

low critical temperatures (CO 2 ). Some power ‐ generating

plants using such uids have been built [3] but in most

cases the published literature consists of semi ‐ analytical

or numerical studies. A 2006 analysis of solar trough

ORC electricity generating systems (available at http://

www.nrel.gov/docs/fy06osti/39433.pdf) concluded that

such plants with 1 – 10MW capacity would be economi-

cally attractive for isolated communities in Africa and the

Middle East. Grid connected customers in the US

with large loads concerned about reliability and paying

high prices for peak electricity are also potential custo-

mers for such systems. Liu et al. [4] analyzed the effect

of working uids (wet: water, ethanol; dry: HFE7100,

n ‐

results show the existence of an optimum evaporation

pressure for each of the four steps. They also indicate

that an increase of the net power output decreases the

exergetic efciency and increases the heat exchangers ’

surface. On the other hand, Cayer et al. [8] analyzed

the performance of a transcritical CO 2 cycle with

specied heat source temperature (100°C) and mass

owrate as well as heat sink temperature (10°C). They

used six performance indicators (thermal efciency,

specic net output, exergetic efciency, total UA and

surface of the heat exchangers as well as the relative

cost of the system) and three independent parameters

(maximum temperature and pressure of the cycle as

well as the net power output). Their results show that it

is impossible to simultaneously optimize all six per-

formance indicators. They nally optimized the cycle

parameters by minimizing the acquisition cost of major

components per unit output

($kW − 1 ) and compared

such optimum cycles for

three working

uids (CO 2 ,

ethane, R125).

Recently, Lakew and Bolland [9] analyzed the per-

formance of the following working uids: R134a,

R123, R227ea, R245fa, R290 and n ‐ pentane. Their

evaluation is based on power production capability

and equipment size requirements. They used a sub-

critical Rankine cycle without superheating, specied

the heat source temperature in the range of 80 – 200°C

and used the evaporator pressure as independent

parameter. The performance parameters examined are

power output, exergetic efciency, heat exchanger area

and turbine size factor. The results of this study show

that the selection of working uids depends on the type

of heat source, the temperature level and the design

objective. The latter can be either the maximum power

output or the smallest component size (heat exchanger

or turbine). It was shown that maximum power

is obtained for an optimal evaporator pressure.

Furthermore, a working uid may have the smallest

turbine size factor but require a large heat exchanger

area. The authors concluded that an economic study is

necessary to determine which working uid is the most

appropriate.

Mago et al. [10] calculated the exergy destroyed in

an ORC using R113. They established that most of the

exergy destruction occurs in the evaporator. They also

showed that the total exergy destruction decreases with

increasing evaporator pressure and with decreasing

difference between the temperatures of the heat source

and the working uid in the evaporator. Guo et al. [11]

presented a comparative analysis of natural and

conventional working uids for use in transcritical

Rankine cycles using a low ‐ temperature (80 – 120°C)

geothermal source. Their results show that R125 gives

the best thermodynamic and techno ‐ economic perfor-

mance. For source temperatures above 100°C, R32 and

R134a also show better performances than CO 2 , which

was used as a base line. Chen et al. [12] presented a

review of the organic and supercritical Rankine cycles

pentane and isentropic: R11, R123,

benzene) on the performance of ORCs and reported

that the thermal efciency of such cycles is a weak

function of the critical temperature. They also indicated

that using a constant heat source temperature can

result in considerable design differences with respect to

the actual variable temperature of nite heat sources

such as geothermal or waste streams. Madhawa

Hettiarachchi et al. [5] used the ratio of the total heat

exchanger area to the net power output as the criterion

for the ORC design and evaluated the optimum cycle by

varying the evaporation and condensation temperatures

as well as the velocities of the geothermal source and the

cooling water. They compared the optimum cycle per-

formances for four working uids by xing the gross

power output of the cycle and found that ammonia

minimizes the chosen design criterion but its corres-

ponding rst and second law efciencies are lower than

those obtained with HCFC 123 and n ‐ pentane. These

two studies do not consider superheating of the working

uid. On the other hand, Saleh et al. [6] performed

a thermodynamic analysis of 31 pure working uids

for ORCs with and without superheating, operating

between 100 and 30°C. They found that the highest

thermal efciencies are obtained with dry uids in

subcritical cycles with regenerator. They also performed

a pinch analysis for the heat transfer between the source

and the working uid and reported that the largest

amount of heat can be transferred to a super ‐ critical

pentane,

iso

‐

uid.

Similarly, Roy et al. [7] analyzed the performance of

a Rankine cycle with superheating using a mixture of

ammonia and water for

uid and the least to a high

‐

boiling subcritical

xed source and sink temper-

atures. Their methodology includes four steps: energy

and exergy analyses,

nite size thermodynamics and

calculation of

the heat exchangers ’

surfaces. Their

872

Int. J. Energy Res. 2012; 36:871

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DOI: 10.1002/er

Thermodynamic analysis and optimization of power cycles

M. Khennich and N. Galanis

for the conversion of low ‐ grade heat as well as selec-

tion criteria for working uids. Types of working

uids, the inuence of latent heat, density, specic heat

and other thermodynamic properties (at the critical

and freezing points) as well as the effectiveness of super-

heating, the stability, safety and environmental impact

were discussed. They considered 35 potential working

uids and grouped them based on the values of their

critical temperature and the inverse of the slope of

the saturation vapor curve on the T − s diagram. They

concluded that there is no uid that meets all the criteria

for heat sources with different temperatures.

Despite these and other analogous studies, the thermo-

dynamic analysis of power cycles using low ‐ temperature

heat sources with a specied mass owrate (such as

industrial waste heat) and a heat sink of xed inlet tem-

perature is not complete. In the present paper, we illus-

trate certain properties of such cycles with both saturated

and superheated conditions at the turbine inlet through a

case study using ve working uids (R134a, R123,

R141b, ammonia and water). Their potential for power

production in a speci

evaporator. Turbine and pump efciency is 0.80, which

is assumed to be the same for all considered working

uids. The temperature at the turbine inlet and the

condensation temperature are varied by changing the

value of the temperature difference DT. The tempera-

ture – entropy diagram of the system used to recover

energy from the low ‐ temperature gas stream is shown in

Figure 2, which illustrates a case with superheated uid

at the turbine exit. It should be noted however that for

some working uids and high values of the evaporating

pressure state 2 can be in the two ‐ phase region.

The basic equations used to model the cycle express

mass and energy balances for each component. The

assumptions are the following:

•

Each component is considered as an open system

in steady ‐ state operation;

c range of evaporation pressure is

evaluated. Speci

cally, we show that for these conditions

the acceptable range of evaporation pressures has upper

and lower bounds, which approach each other as the net

power output of the cycle increases. As a result, the net

power output of the cycle cannot exceed an upper limit

W n ; max . It is also shown that for each possible value

of the net power output there exists an optimum value

of the evaporation pressure, which minimizes the total

thermal conductance of the two heat exchangers.

Furthermore, the turbine size factor and the effect of the

temperature difference DT on the volume ow ratio

at the turbine inlet and outlet are determined for the

conditions minimizing the total thermal conductance

UA t . Finally, an exergy analysis of the optimum cycle

identies the major irreversibility sources.

Figure 1. Schematic diagram of system under consideration.

2. SYSTEM DESCRIPTION

AND MODEL

Figure 1 illustrates the schematic diagram of a basic

system (ORC,

critical cycle or system using a

mixture of uids) used to recover energy from a low ‐

temperature gas stream. It is similar to the superheated

Rankine cycle. The heat source is an industrial waste

gas idealized as air at a temperature of T s,in = 100°C

with a volumetric owrate of 1.2millionm 3 h − 1 (for

atmospheric pressure and 100°C the corresponding

mass owrate is M s ¼ 314 : 5kgs 1 ). The cooling uid

in the condenser is water at T p,in = 10°C (the annual

average temperature of the water of the St. Lawrence

river). The working uid receives heat at a relatively

high pressure in the evaporator, expands in a turbine,

thereby producing useful work, and rejects heat at a low

pressure in the condenser.

trans

‐

is then pumped to the

Figure 2. Temperature

–

entropy diagram.

873

Int. J. Energy Res. 2012; 36:871

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DOI: 10.1002/er

M. Khennich and N. Galanis

Thermodynamic analysis and optimization of power cycles

• The kinetic and potential energies as well as the

friction and heat losses are neglected;

• At the exit from the condenser the working uid is

saturated liquid;

depend on those of

the two independent parameters

P ev and DT.

For the exergy analysis of the system, the mass

owrate of the working uid in the cycle is required.

The latter is calculated by xing the net power output

W n of the system or, more specically, its non ‐

dimensional value α which is obtained by dividing

•

The pinch for the condenser, equal to (T g – T p,pr )

when state 2 is superheated vapor and to

(T 2 – T p,out )whenitisatwo ‐ phase mixture, is set

equal to DT/2 while that for the evaporator,

DT 5* =(T s,sc – T 5* ), is required to be greater than,

or equal, to DT/2;

W n

by the following reference quantity:

W ref ¼ M s Cp s T s ; in T p ; in

1 T p ; in = T s ; in

(9)

•

The specic heat of

the source and sink is

W ref is evaluated by considering a Carnot process

operating between the inlet temperatures of the heat

source and sink. With the adopted conditions, the

value of this reference quantity is 6861kW. The pro-

duct of the mass owrate, the specic heat and the

temperature difference is higher than the actual heat

extracted from the heat source, whereas the Carnot

efciency is higher than that of the actual cycle using

the specied heat source and sink. Therefore, the

values of α will be considerably lower than one. From

the previous energy analysis, which determines the

specic net power output, the mass owrate of the

working uid is calculated for a given value of α :

m ¼ a W ref

assumed to be constant;

•

The specic volume of the working uid remains

constant during pumping;

•

Finally, the liquid content at the exit of the

turbine is required to be less than 5% to limit the

effect of liquid droplets on the turbine blades.

Since the quantities M s , T s,in , T p,in , η T and η P are

xed, the choice of a value for DT determines state 4

and T 1 . Under these conditions the evaporation pres-

sure can vary but its value is constrained by the im-

posed restrictions on the quality at the exit from the

turbine and the evaporator pinch. For any value of this

pressure that satises these two requirements the entire

cycle is xed and its performance can be calculated

using the following equations taking into consideration

the assumptions already presented:

= w n (10)

The mass owrate of the working uid is therefore

proportional to α (or, equivalently, to the net power

output) and inversely proportional to w n which, as

established earlier, is a function of P ev and DT. Thus

m = α f(P ev ,DT).

The mass owrate of the cooling water is obtained

from the energy balance for the phase change in the

condenser:

Q 4g ¼ _ mh g h 4

•

For the pump:

η P ¼ n 4

P ev P C

(1)

h 5 h 4

w P ¼ h 5 h 4

(2)

¼ M p Cp p T p ; pr T p ; in

(11)

•

For the turbine:

The thermal conductance UA 4g for this part of the

condenser can then be obtained using the corres-

ponding logarithmic difference:

Q 4g ¼ UA4 g Δ T ln ; 4g (12)

An analogous approach is applied to the desuper-

heating part of the condenser and results in the

determination of T p,out and UA 2g . When state 2 is a

two ‐ phase mixture the temperature difference

(T 2 – T p,out ) is set equal to DT/2. The mass owrate

of the cooling water and the thermal conductance of

the condenser are obtained from the corresponding

energy balance and logarithmic temperature difference

(equations similar to Equation (11) and (12)). Similarly,

the three unknown temperatures (T s,pr , T s,sc , T s,out )and

the corresponding thermal conductances for

h 1 h ð Þ

h 1 h 2 ; is

η T ¼

(3)

w T ¼ h 1 h 2

(4)

•

For the evaporator:

q ev ¼ h 1 h 5

(5)

•

For the condenser:

q C ¼ h 2 h 4

(6)

•

The specic net power output is:

w n ¼ w T w P

(7)

the three

•

The thermal ef

ciency of the cycle is:

parts of

the vapor generator

(UA 11* ,UA 1*5 ,UA 5* 5)

can

determined

from equations

similar

w n

q ev

η th ¼

(8)

Equations (11) and (12).

Since the potential and kinetic energies have been

neglected, the exergy of the working and external uids

at any state can be calculated from:

e ¼ h h 0

According to the arguments in the paragraph pre-

ceding Equation (1), the thermodynamic properties of

the working uid as well as the values of w n and η th

Þ T 0 s s 0

(13)

874

Int. J. Energy Res. 2012; 36:871

–

DOI: 10.1002/er

Thermodynamic analysis and optimization of power cycles

M. Khennich and N. Galanis

3. WORKING FLUIDS

The dead state, indicated by the subscript 0, is at

atmospheric pressure and the xed temperature

T p,in = 10°C of the water entering the condenser. The

exergy destruction rate in any of the system ’ s compo-

nents is then calculated from the following exergy

balance equation:

E d ¼ X

The choice of the working uids was based on their

thermodynamic characteristics and their environmen-

tally benign nature. Working uids for systems with

low or intermediate temperature sources must satisfy

several safety, environmental, performance and eco-

nomic criteria [12]. Among the safety aspects, amm-

ability, toxicity and auto ‐ ignition are particularly

important. Environmental criteria include the ozone

depletion potential

Þ X

out

Þ W

m in e in

m out e out

(14)

The total exergy destruction E d ; t , i.e. the summation

of the exergy destruction by all its components, is non ‐

dimensionalized by dividing it by the exergy of the heat

source:

(ODP) and the global warming

potential (GWP).

Based on these considerations, the following working

uids R134a, R123, R141b, ammonia and water are

used in the present study. Their thermophysical, safety

and environmental properties are compared and pre-

sented in Table I. It should be noted that R123 and

R141b will be phased out by 2030 due to their non ‐ zero

ODP [12]. From a safety point of view water and R134a

are the best, while ammonia is the worst. From an

environmental point of view ammonia and water are the

best. Water has been included in the present study for

the purpose of comparison although it is known that it

is not a good working uid for low ‐ temperature systems

such as the one under consideration.

b ¼ E d ; t = M s e s ; in Þ

(15)

A small value of β is an indication that the system

approaches thermodynamic perfection.

The preliminary design of the turbine can be obtained

following a study by Macchi and Perdichizzi [13] by

calculating the turbine size parameter SP, which accounts

for the actual turbine dimensions, and the turbine isen-

tropic volume ow ratio V RT,is , which accounts for

compressibility effects during the expansion:

0 : 5

SP ¼ V T ; 2is

= ð 1000 Δ h is Þ

(16)

V RT ; is ¼ V T ; 2is = V T ; 1 (17)

The study by Macchi and Perdichizzi [13] states that

the results obtained by optimizing a particular turbine

can be used for other turbines with the same specic

speed, provided they have the same SP and V RT,is

parameters.

Based on the previously presented relations between

the dependent variables (P C , thermodynamic proper-

ties of the working uid, w n , m) and the independent

parameters ( α , P ev , DT) it follows that for the condi-

tions under consideration all the UAs, the mass ow

rate of the sink, β and SP are functions of the same

three independent variables which can take different

values compatible with the previously specied con-

straints on x 2 and DT.

The numerical model of the system was solved using

the EES code [14], which includes thermodynamic

properties for a large number of natural and manu-

factured uids. The present model and calculation pro-

cedure were successfully validated by comparing their

results with those published by Liu et al. [4] and by

Madhawa Hettiarachchi et al. [5] (see the Appendix).

4. RESULTS AND DISCUSSION

The results presented here have been calculated for the

ve previously mentioned working uids with T s,in =

100°C, M s ¼ 314 : 5kgs 1 , T p,in = 10°C. The range of

values for the temperature difference DT is 5 – 15°C.

The efciency of the turbine and pump is xed at 0.80.

4.1. Effect of the evaporation pressure

and DT

Figure 3 shows the effect of the evaporator pressure on

x 2 (when x 2 < 1 this ratio is the quality of the working

uid at the exit of the turbine) and on the temperature

pinch in the evaporator (DT) for R134a, α = 0.05 (or

equivalently W n ¼ 343 : 1kW ) and DT = 5°C. When

P ev is low the working uid at state 2 is superheated

vapor (this is indicated by x 2 > 1). As P ev increases

state 2 approaches the saturation curve and eventually

the uid at 2 becomes a mixture of vapor and liquid; its

Table I. Thermophysical, environmental and safety characteristics of working uids.

Molecular weight

(kgk − 1 mol − 1 )

ASHRAE 34

safety group

GWP

(100 year)

Fluid

Formula

NBP (°C)

T cr (°C)

P cr (MPa)

ODP

Nature

R134a

CH 2 FCF 3

102.03

− 26.1

101.03

4.06

1300

Isentropic

R123

CHCl 2 CF 3

152.93

27.8

183.68

3.67

0.012

120

Isentropic

R141b

CH 3 CCl 2 F

116.95

32.0

204.20

4.25

0.086

700

Isentropic

Ammonia

NH 3

17.03

− 33.3

132.25

11.33

Wet

Water

H 2 O

18.02

100.0

373.98

22.06

Wet

875

Int. J. Energy Res. 2012; 36:871

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DOI: 10.1002/er

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